Guitar pick man not toothpick lol
I've never fitted a TOM to a neck with a radius other than 12", so just get a piece of paper, and a piece of card about business card thick, and if you can't shim a neck with those, then you ain't sh*t homeboy!
You cut out a strip from the card that will fit only around the two neck screws that are closest to the neck pickup, place it between neck and body in the pocket and you have a neck angle to bring the action down on the high frets.
If it's ridiculously high action, you might need a pick but i've never had to use them.
I'm no professional guitar tech, but i have shimmed in excess of 15 guitars, always used the card method and never noticed any sound change, just a big change in playability.
Using a pick for shimming isn't a good idea, if you have to, use three instead of one. If you just used one, the pick would have to go in the centre of the neck pocket, so you have a gap either side, not good when you're scewing the neck in i wouldn't have thought. Drill a hole in two picks so they will fit with the neck screws and into the pocket and pop the remaining one in the centre, equal pressure in the pocket can't be bad.